Are species distributions clumped across the landscape?
Possible Null Hypotheses:
\[s^*(m) = \displaystyle\sum^{K}_{i=1} \left[ 1 - \frac{\binom{M - L_i}{m}}{\binom{M}{m}} \right] \]
where:
niter <- 1000
birds.s <- birds
out.s <- matrix(data = NA, nrow = niter, ncol = quads)
for(ii in 1:niter){
birds.s$quadrat <- sample(1:quads, size = nrow(birds), replace = TRUE)
nsps <- birds.s |>
count(Species)
pres <- birds.s |>
group_by(Species) |>
summarise("pres" = length(unique(quadrat)))
out.s[ii,] <- sm(quads, nsps$n, pres$pres)
}